Covid-19 in stock markets: a Complexity perspective

This paper aims to analyze the effects of Covid-19 on financial markets from the perspective of Complexity. The Covid-19 pandemic has caused turmoil in financial markets and is already one of the most important financial crises in history, causing a fall in several stock markets as well as great volatility. Unlike past crises, which in most cases were caused either by problems of fiscal deficits or in the financial system, this crisis has its origin in an epidemic disease, which occurred in Wuhan, China, and quickly spread across the globe affecting transport networks, commerce and finance, and will affect the public debt of many countries. This is a systemic situation in which there is a need to consider several interconnected systems, financial instability and high financial risk, something that econophysics and some complexity theorists already do. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 May 2020 doi:10.20944/preprints202005.0056.v1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license. Therefore, this paper intends to show, theoretically, the systemic and complex character of the recent financial crisis caused by Covid-19.


INTRODUCTION
The outbreak of the coronavirus 2 (SARS-CoV-2) respiratory syndrome has already 2435876 confirmed cases and has caused 167639 deaths worldwide until April 20, 2020, and numbers continue to grow (WHO, 2020). The first case of  was registered in China in December 2019, and since then, the virus has spread quickly around the world (Wang et al., 2020). The World Health Organization (WHO) classified it as a pandemic on March 11, 2020. Therefore, this paper intends to show that the complexity approach, used to analyze financial markets as an interconnected system and subject to great variations, is a theoretical option for understanding the financial crisis caused by Covid-19. The main ideas originating from this approach will be demonstrated, in particular the analysis of Econophysics and the use of power laws and complex networks. The goal is to show that the Covid-19 financial crisis can be characterized as a complex phenomenon.

ECONOPHYSICS AND POWER LAWS
Econophysics is a neologism used in the branch of Complex Systems from Physics seeking to make a complete survey of the statistical properties of financial markets, using the immense volume of available data and the methodologies of statistical physics (Mategna and Stanley, 1999). The term Econophysics was coined by Stanley et al. (1996) when they analysed the Dow Jones index and found that stock returns followed a power law distribution, contributing to the emergence of this new research field.
The idea that stock returns follow a power-law format is recurrent in Econophysics (see, for example, Stanley et al., 1996, Lux, 1996, Mantegna and Stanley, 1999or Gabaix, 2009, among many others). One power-law can be defined as = , where k and α are constants, asymptotic values of a variable x, like → ∞ (Newman, 2004). Thus, power-laws have played an important role in economics to the extent of warranting an extensive article in the Journal of Economic Perspective (JEP), in which Gabaix (2016) demonstrates their applications in relation to finance, city size, executive salaries and macroeconomics, very different subjects.
While some economic models and hypotheses, such as the efficient market hypothesis of Fama (1970), Malkiel and Fama (1970) and Fama (1991) and the Black and Scholes (1973) model have assumed that returns follow a normal distribution, Econophysics has contradicted this since its emergence: if the distribution of stock returns follows a power-law distribution, this implies that large fluctuations in stock exchanges can occur. Accepting that financial markets are subject to wide variations can contribute to mitigation of these financial instabilities or even prevent them (Pereira et al. 2017).

COMPLEX NETWORKS
At the end of the 1990s, with the discovery of new network topologies such as small world (Watts and Strogatz, 1998) and free of scale (Barabasi and Albert, 1999), the study of complex networks appeared. 1 Complex systems, in general, involve innumerable elements organized in structures that can exist or coexist, in different scales (Pereira, 2013). Most of their main characteristics emerge from interactions between their constituent parts, and cannot be predicted from an isolated understanding of each of these parts (Costa et al., 2007). In this context, complex networks can be located at the intersection of graph theory and statistical mechanics, involving several knowledge areas, and therefore, their study can be considered as a multidisciplinary approach (Pereira, 2013).
It can also be highlighted that complex networks have contributed to the economy by proposing new methods, techniques and properties (Schweitzer et al. 2009). In this context, one research area which benefited from these new approaches is finance, for which network theory enabled measurement of the probability of systemic risk, due to the interconnections and interdependence between the agents of a given 1 The structure of a complex network is represented in the same way as a graph in a set R, which, in the case of networks that have no weights in their connections, is defined by = { 1 , 2 , 3 , . . . , } the nodes (or vertices) and = { 1 , 2 , 3 , . . . , }, the edges or connections that link pairs of nodes. The numbers = | | and = | | are considered as the quantities of elements in and respectively (Newman, 2018). system or market, in which the insolvency or bankruptcy of a single entity (or group of entities) can cause chain failures (Jackson 2010(Jackson , 2014. In this context, Boss et al. (2004) showed that before a financial crisis, the world banks' payment systems were interconnected and had a probability distribution in the form of a power-law, meaning that a large part of the transactions involving those payment systems was concentrated in a very small number of banks, while many others traded a smaller amount.
Economists consider the importance of a payment institution according to the volume of resources it administers. However, the concept of centrality 2 extracted from complex networks helps to classify the importance of these institutions based on how central they are in a given network (in that case, the financial system). Battiston et al. (2012bBattiston et al. ( , 2016 propose that instead of considering financial institutions "too big to fail" in terms of default risk, they can be considered "too central to fail", i.e. monitoring the centrality of a financial institution rather than its size. This may better explain how a crisis can spread in a banking system, since negative shocks to central financial institutions can cause a system-wide contagion effect. When it is discovered that there are too many central markets to break, this implies that some relevant financial markets such as those of the European Union or the United States have a high centrality and any disturbance in them can affect, practically, the entire network which is connected to them (Pereira et al. 2019).
Complex networks have influenced analysis in finance, as in, for example Haldane and May (2011), who analyzed the banking system as an ecological network susceptible to financial risks due to its topology. Diebold and Yilmaz (2011), using 2 An important property of networks is the centrality, which quantifies the importance of the vertices (or edges) that are in a networked system. In complex networks there is a wide variety of mathematical methods and measures of centrality of vertices that focus on different concepts and definitions of what it is to be central in a network. A simple measure of centrality in a network is the degree of vertex, which represents the number of edges connected to it, being considered one of the most important network metrics (Newman, 2018).